Hinged beam dynamics

TL;DR

This paper establishes the existence and uniqueness of high-regularity solutions for a nonlinear fourth-order wave equation modeling hinged beam vibrations, using Galerkin approximation for large-time analysis.

Contribution

It provides the first rigorous proof of large-time existence and uniqueness for such nonlinear beam vibration problems with high regularity solutions.

Findings

Proved large-time existence of solutions

Established uniqueness of solutions

Applied Galerkin approximation method

Abstract

In this paper we prove large-time existence and uniqueness of high regularity weak solutions to some initial/boundary value problems involving a nonlinear fourth order wave equation. These sorts of problems arise naturally in the study of vibrations in beams that are hinged at both ends. The method used to prove large-time existence is the Galerkin approximation method.